Amazon is the latest internet company to enter the streaming music market, debuting its Prime Music service in the US today.

It is being bundled into the existing Amazon Prime subscription service rather than launched as a standalone product.

That means customers paying $99 a year for free shipping, streaming TV and films and Amazon's "lending library" of e-books will now also be able to access Prime Music's catalogue of streaming songs.

The service is advertising-free, with no restrictions on how often individual songs can be played. Prime Music will work on iOS, Android, PC and Mac devices, as well as Amazon's Kindle Fire tablets. Customers will be able to download songs for offline listening too.

Prime Music's catalogue is considerably smaller than rival services, though. Amazon has "over a million songs" available at launch in Prime Music. By contrast, Spotify and Deezer both claim to have more than 30m songs available.

In Amazon's case, the small size of its catalogue may be partly a bet that a more mainstream audience of fans don't mind a smaller pool of music to choose from.

Prime Music is launching with hundreds of "Prime Playlists" created by Amazon's editorial team, grouped by genre (Pop, Alternative & Indie Rock) as well as context (Happy & Upbeat, Party Time & Entertaining, Work, Study & Reading etc.)

Many of those playlists offer a "top songs" guide to individual artists, from Whitney Houston and Prince to Franz Ferdinand and The Strokes. It's an indication that Amazon sees Prime Music as focused more on back catalogues than current hits.

That backs up reports in May, when BuzzFeed claimed that the upcoming service "will not include recent releases but instead restrict its catalog to songs and albums that are six months old and older".

This week, the New York Times claimed that Prime Music "will omit most new releases" but also suggested that Amazon has only signed licensing deals with two of the three major labels – Sony Music and Warner Music Group – with Universal Music holding out for better terms.

Other streaming services that have announced figures include Deezer, which has 16m active users including 5m paying subscribers, and Rhapsody, which has 1.7m paying subscribers across its US service and its Napster subsidiary elsewhere in the world.

Beats Music, which was recently bought by Apple as part of a $3bn acquisition of its parent company Beats Electronics, has 250,000 paying subscribers. Meanwhile, the size of rivals from Microsoft (Xbox Music), Sony (Music Unlimited) and Google (All Access) is unknown.

Amazon's streaming launch comes at a time when the company is embroiled in controversy over its distribution relationships with other entertainment rightsholders.